There's also a version where you lie on your chest on a bunch, and use dumbbells. That seems like it would be awkward, not enough room to extend arms fully. Should I give that one more of a look, or is the cable version good enough?

What's the right form for the exercise? I've seen a vid where the guy has the rope coming out thru the bottom of his grip, and he ends the move in a sort of "double-bicep" pose, with his fists a little above and out from his ears. Saw another where the guy had the rope coming out thru the top of his grip, and he pulled the rope more or less toward his chin, taking care to keep his elbows high, above his wrists. Which one is right? Or is there a third, better option.

What else should be said about Face Pulls?

“War is the remedy our enemies have chosen. Other simple remedies were within their choice. You know it and they know it, but they wanted war, and I say let us give them all they want.”
― William Tecumseh Sherman

What you're trying to hit determines technique. If you're just looking for scapular retraction/horizontal abduction, then just find an angle that allows you to squeeze your shoulder blades together well against the resistance (with elbows out). If you're looking to add external rotation, then you need to rotate your arms up into the "double bicep" position as you pull. You might need to tinker around with different ways of pulling to see what hits the areas you want to get.

All the versions are useful to a degree. Honestly, I'd do face pulls above the head and reapers....(search here for that definition) Otherwise, FP's are just part of a huge rotation so upper back pieces that you can rotate. If there are two I think shoudl be on everyone's list..(mostly everyone) it's reapers and Incline bench DB rows with a hold. i think these do what Face pulls purport to do but in a way that you can feel when you press.

"He who knows only his own side of the case knows little of that." JS Mill

“War is the remedy our enemies have chosen. Other simple remedies were within their choice. You know it and they know it, but they wanted war, and I say let us give them all they want.”
― William Tecumseh Sherman

Basically, it's a behind the neck lat pull down. You should take a grip where your forearms remain vertical through the pull. Use a weight you 20 reps with a BTN pull down.

Pull the bar to just about where your upper arm fdrops below horizontal. On most of us that means the bar is slightly below the crown of your head or the occipital bun.
Do them slow and controlled. You should be able to stop the bar at any point in the stroke and hold for time. I like a 3:1:3 cadence with a slight pause at teh bottom where you squeeze your shoulder-blades back, down and together activating all the rhomboids, upper and lower traps. Holding and squeezing them at tope and bottom as well as keeping continuous tension of the bar will ensure these really teach you to stay tight.

Jack can probably add to this, but it's how I've done them and passed them on to other people.

"He who knows only his own side of the case knows little of that." JS Mill

I like standing TRX face pulls using some different angles - to face, y pulls, 90 degrees at elbow. 15- 20 total reps per set and using different angles as I get tired in one plane. Feels good, man. Don't get the same feeling from prone rowing or batwings.

I feel my mid-back and traps in a way that I don't get with anything else.

I don't think there is a single way to do this type of pre/re-hab exercise...
Look at the the basic YTLW external rotator movements. Then think of 'face pulls' with a cable machine as YTLW movements against resistance.

...When you're sick of that get back to highpulls, cleans, and kettlebell snatches.

What lies behind us and what lies before us are tiny matters compared to what lies within us.
Ralph Waldo Emerson